A353191 Expansion of e.g.f. 1/(1 - Sum_{k>=1} mu(k) * x^k / k), where mu() is the Moebius function (A008683).

1, 1, 1, -2, -22, -134, -418, 1044, 35352, 371256, 2662872, 2256, -348450672, -7383337584, -85166363280, -224652273504, 17983453809024, 500248545941376, 7414246148833152, 13911378371907840, -2620344425592796416, -85017815816225598720, -1321651042532303189760

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} (k-1)! * mu(k) * binomial(n,k) * a(n-k).

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[(k - 1)! * MoebiusMu[k] * Binomial[n, k] * a[n - k], {k, 1, n}]; Array[a, 23, 0] (* Amiram Eldar, Apr 30 2022 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, N, moebius(k)*x^k/k))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (j-1)!*moebius(j)*binomial(i, j)*v[i-j+1])); v;

Crossrefs

Cf. A008683, A300663, A352869, A353189.

Sequence in context: A255866 A330900 A356341 * A062180 A244719 A084399

Adjacent sequences: A353188 A353189 A353190 * A353192 A353193 A353194

Keyword

sign

Author

Seiichi Manyama, Apr 29 2022

Status

approved